Download Motions of the Sky

Motions of the Sky
The most rapid motions of the celestial objects are the daily motions, which are caused by the
rotation of the earth. We will call these motions “apparent” since the objects involved seem to be
moving across the sky, but the real cause of the motion is the daily spin of the earth on its axis.
The earth spins to the east, going around once in 24 hours. So Spokane is rotating toward New
York. When viewed from above the earth looking down on the north pole, this would be a
counterclockwise motion. In the discussions below, we assume that all observations are made
from the Spokane area. Observations can be different in other locations on the earth, especially in
the southern hemisphere. Since the earth rotates 360O in 24 hours, it rotates (360O/24 hour) =
15O/hour. This is read 15O per hour or 15O in one hour. The apparent daily motion of the sun (see
below) is due to this rotation of the earth.
Daily Motion of the Stars
The stars move in their apparent daily motion as if they were all attached to an imaginary
spherical shell, called the celestial sphere. As we look into the northern sky from our position on
earth, this appears to be a counterclockwise motion, all stars moving in circles around the
(almost) stationary star Polaris (the North Star). Polaris appears nearly stationary, because the
spin axis of the earth is pointed almost directly at Polaris. In the Spokane area, Polaris is 47.5O
(nearly 5 fists) above the northern horizon. This is because Spokane is at 47.5O north latitude
(47.5O north of the equator). At the simplest level of understanding, the stars go one complete
circle (360O) around Polaris in 24 hours. Observations of the Big Dipper at one hour intervals
during an evening will show this motion quite clearly. The slower, seasonal part of star motion is
discussed below.
When we are looking south in the sky, stars appear to move left to right, or east to west, across
the sky. They rise somewhere on the eastern horizon and set somewhere on the western horizon,
but we seldom watch a single star move all the way across the sky. The stars are highest above
the horizon when they are due south. In 24 hours, the stars make one complete rotation. See
seasonal star motions below.
Seasonal Motion of the Stars
If the stars made exactly one complete rotation (360O) around the earth in 24 hours in their
apparent daily motion as discussed in the previous two paragraphs, the stars would appear in the
same positions each night. But the stars do change positions slowly as the seasons change. In
fact, the stars travel nearly 361O in 24 hours. As we look into the north sky at the same time on
successive nights, the star field is rotated almost 1O counterclockwise around Polaris on the
second night. As we look into the southern sky, we see the star field shifted 1O farther west each
night. This continues all year long, so that at the end of the year, the star field has done one more
complete rotation than if the stars only moved 360O in 24 hours. Thus we see different stars in the
evening sky in different seasons of the year, and the whole sky rotates past us in a year’s time.
The effect in the northern sky is that the big Dipper appears in different places in its circle around
Polaris in different seasons. It is higher in spring and summer than it is in fall and winter.
Daily Motion of the Sun
In its apparent daily motion, the sun acts like a star, rising somewhere on the eastern horizon,
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moving across the southern sky, and setting somewhere on the western horizon. It is highest for
the day when it is due south, which is approximately 12:00 PM, but can be as early as about
11:30 AM and as late as 12:10 PM in Spokane. On average, the sun makes one complete rotation
around the earth in 24 hours in its apparent daily motion, but the actual time varies a little bit
from day to day. This means that the sun moves across the sky at a rate of 15O each hour. If we
assume the sun is due south at 12:00 PM (noon), we can say that it is 15O east of south for each
hour it is before noon, and 15O west of south for each hour it is after noon.
Seasonal Motion of the Sun
The sun makes a different arc across the sky in different seasons. On about June 22 (the
summer solstice), the sun rises farthest north of east, makes its highest arc across the sky, and sets
farthest north of west It gets 66O above the southern horizon at noon and is above the horizon
about 15 hours. Each day after the summer solstice, the sun moves a little to the south, making a
lower arc across the sky. By the autumn equinox on September 23, it is rising due east, it is 42.5O
above the southern horizon at noon, it sets due west, and it is above the horizon 12 hours. After
the autumn equinox, it continues its journey southward until the winter solstice, December 22.
On this day, it rises farthest south of east, makes its lowest arc across the sky, and sets farthest
south of due west. It only gets 19O above the horizon at noon, and it is in the sky only about 9
hours. Following the winter solstice, the sun starts moving back northward, making a higher arc
each day. By the vernal equinox, March 20, it behaves exactly as it did on the autumn equinox,
rising due east, setting due west, and staying above the horizon for 12 hours. Then it continues
northward until the summer solstice, and starts the process over again. See the attached figure
labeled “Daily Path of the Sun in Different Seasons.”
In its seasonal motion, the sun “appears” to move through the star field along a path called the
ecliptic. The “Signs of the Zodiac” are 12 constellations that lie along the ecliptic. This motion is
really due to the eastward motion of the earth around the sun in its yearly orbit. This apparent,
seasonal or yearly motion of the sun is mostly eastward through the star field, but the sun swings
to the south in the winter and back to the north in the summer.
The Daily motion of the Moon
On any given day, the moon moves across the sky much like a star or the sun. It rises
somewhere on the eastern horizon, moves across the southern sky reaching it high point for the
day when it is due south, and sets somewhere on the western horizon. However, like the sun, the
moon makes different arcs across the sky on different days, and goes through essentially the
same pattern of change in one month that the sun does in one year. The actual daily arc depends
on both the phase and the season of the year. For example, the full moon makes a high arc across
the sky in the winter, but a low arc in the summer.
Monthly Motion of the Moon
While the sun moves 15O each hour in its westward, apparent daily motion, the moon moves
about 14.5O each hour. Thus the moon falls behind the sun about 0.5O each hour, or 12O each day.
The result is that the moon seems to move eastward relative to the sun and relative to the stars.
This motion is really caused by the moon’s orbital motion eastward around the earth. As the
moon orbits the earth, it passes through the star field along nearly the same path (the signs of the
Zodiac) that the sun does in its seasonal motion. It takes the moon 29.5 days to fall a complete
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lap behind the sun, and this is the duration of the 360O lunar cycle. So the moon falls behind the
sun by (360O/29.5 days) = 12.2O/day. Remember that this is an eastward motion on the celestial
sphere, in the opposite direction to the daily, westward motion.
As the moon changes its position in the sky relative to the sun, it changes its phase. At the
start of the cycle, just after new moon, it is close to the sun and moving eastward away from it, so
it is a waxing crescent. When it gets 90O east of the sun it is a first quarter half moon. (It is one
quarter of the way through the cycle and it is half lit.) It continues moving eastward through the
waxing gibbous phases, until it is 180O from the sun and is full. Since the full moon is opposite in
the sky from the sun, it rises at sunset and sets at sunrise. This is the moon that can get into the
earth’s shadow for a lunar eclipse.
This first half of the cycle is shown in the attached figure labeled “Waxing Moon at Sunset.”
The figure is drawn as if you went out each night at sunset and found the moon. It illustrates the
eastward shift of the moon as it falls behind the sun each day and the changing phase associated
with this eastward shift.
The figure labeled “Waning Moon at Sunrise” illustrates the second half of the lunar cycle.
In this figure, we imagine that we go out each morning at sunrise and observe the moon. The
moon continues its eastward motion relative to the sun, but now it gets closer to the sun each day.
As it does so, it wanes, passing through the waning gibbous phases, the third quarter half moon,
and the waning crescent phases. Finally the moon lines up with the sun as a new moon, which is
not visible to us. The new moon can get exactly in front of the sun to produce a solar eclipse, but
usually it passes above or below the sun and no eclipse is produced.
The moon in its monthly motion moves through the background stars on nearly the same
path that the sun does during the year, the ecliptic. In fact, the moon is never farther than 5O from
the ecliptic. When the moon is near the winter solstice part of the ecliptic, its daily path is like
the December sun. When it is near the summer solstice part of the ecliptic, it behaves like the
June sun. Here is a good example. In December the sun is near the winter solstice part of the
ecliptic. The full moon, on the other hand, is in the opposite part of the sky, 180O away from the
sun. This places it near the summer solstice part of the ecliptic. So in December, the full moon
acts like the June sun, rising north of east, making a high arc across the sky, and setting north of
west. In June, the positions of the sun and moon are reversed. The sun is near the summer
solstice and the full moon is near the winter solstice part of the ecliptic. So in June, the full moon
makes a daily path like the December sun.
Planets
The planets also share in the apparent daily motion caused by the spin of the earth. So on any
given day, they behave much like the sun. Like the sun and moon, they appear in the star field in
the signs of the Zodiac, making the Zodiac the plane of the solar system. The planets slowly
change their positions in the star field in complicated ways that we will not discuss here.
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